The Odds and Ends of Bridge (Part 1)

I. Chance and Probability Theory

The likelihood of the occurrence of any event in Bridge is called a probability. For example, probabilities can refer to the location of specific cards, high card points, or distribution of the suits among the four hands. Probabilities are not guarantees. On one deal or a single play of the cards, calculated probabilities may lead you to an aberrant result, but over the long run probabilities will prove out within a very small variance. The moral of this story is that if you want the probabilities and odds to even out, play more bridge. The usefulness of probabilities is not to determine whether an isolated line of play will work, since if you have only one line of play, it makes no difference what the probabilities are, it either works or it doesn’t! On the other hand, if you have two or more chances to make your contract, and you are able to choose among them, then it is helpful to know which chance is more likely to succeed.

II. Using Probabilities to Help You Find Specific Cards

The underlying math of bridge sees 52 individual cards and each of 4 players having 13 pockets where cards can be located. Each time you identify that “x” pockets of a defender are occupied by certain cards, that defender has fewer empty pockets. If you also know the number of cards in that suit held by the other defender, you can fill up some of his empty pockets. We are only concerned with the opponents empty pockets!

For example, if LHO opens 2 spades and you end up playing a contract in 4 hearts, you can reasonably assume that LHO has 6 of his pockets occupied by spades, so he has now has 7 empty pockets. If Declarer looks at her hand and sees 2 spades and also sees 3 spades in the dummy, she knows that RHO started with 2 spades, so now RHO has only 11 empty pockets. This empty pockets stuff is the backbone of all probability calculations in bridge, called the Law of Vacant Places.

How can we make this useful at the card table? Let’s look at the above example. Assume that the success of the contract depends on locating a specific card in a suit other than spades. Since RHO has 11 empty pockets and LHO has only 7 empty pockets, the odds are 11 to 7 (64%) that RHO will have the card you are looking for. This little calculation can be applied any time you have the distribution in any single suit completely identified between the two opponents.

An adjunct to this principle is called the Law of Attraction. Length in one suit attracts shortness in another suit. Conversely, shortness in one suit attracts length in another suit. In this context, the terms “length” and “shortness” speak only to the relative holdings of a defender in two different suits, predicting that when the defender has length one suit he will have shortness in another suit. This is better explained by example.

Again, looking at our first example, since LHO has length in spades (very likely 6), the probabilities are that RHO has greater length in any other suit. Assume declarer has AJx in diamonds and dummy has K10x in diamonds, a two way finesse. Is it simply a random guess as to who has the Queen of diamonds? On this deal, declarer should always finesse RHO for the diamond queen. Two reasons:

1. Remember the “Law of Attraction?” We reason that LHO with 6 spades is likely to have the least number of cards in the diamond suit. At this point, it doesn’t matter how many more diamonds RHO has, as long as we recognize that the odds are that he will have more. Since RHO is most likely to have more diamonds, he is the most likely to hold the missing Queen of Diamonds (or any other specific diamond for that matter). What is important is not how many diamonds RHO has, as long he has more than LHO. If the seven diamonds break LHO 3 and RHO 4, the odds are 57.1% (4/7) that RHO has the Queen I.

If you remember the Law of Attraction, you don't even have to do the arithmetic or memorize card distribution tables. All you are trying to do is figure out which way to take a 50% finesse and you know the person with more diamonds is the favorite to hold the Queen! We don’t really care what the likelihood of success is, as long it is more than 50%. Alternatively, if your contract requires one of two finesses to work, in either diamonds or hearts, and one goes through RHO and the other through LHO, take the one through RHO for the same reasons. These conclusions come with the usual caveat about "all other things being equal." If you have seen the Q of diamonds fall out of LHO’s hand, don't ignore it!

2. I said two reasons. Here is the second! LHO opened a weak 2 bid. He likely has 6-10 hcps. Let’s say on average 8 hpcs. It is also likely that he has at least 5-6 of those points in spades. We could put a fine point on this, but this is not an arithmetic lesson. With 2 or 3 points outside of the spade suit, the odds are simply better that RHO has partner has the Queen of diamonds. This simply reinforces our decision to take our 2 way diamond finesse through RHO.

I have gone to great lengths (with endless repetition) to make this understandable for those who like to know “WHY?” It is better if you understand the analysis, but even if you forget, if LHO makes a weak 2 bid, just take all your finesses through RHO if you have a choice, and remember to save an entry to the dummy!

This example teaches another good lesson that even seems to escape good players. There is always a cost to entering a competitive auction. That cost is the information (strength, location and distribution) that you furnish by bidding, particularly when there is no substantial likelihood that your side will end up declaring a contract. One of the “Hallmarks” of good players is that they listen to the opponents during the auction and use the information they obtain against them.

Welcome to the Rochester Area Bridge Association

There is now a direct link from the Rochester Area Bridge Club website to Tommy's Bridge Blog. A sincere thanks to RABA for giving me the link. I already have some Rochester area readers, but for those of you who may be checking the site out for the first time, let me give you an overview. I started the site about 9 months ago, and in that time I have made about 40 posts to the site. It is designed primarily for novices and intermediates, but I have had some very good bridge players tell me that they go to the site and that they find my material interesting, thought provoking and a helpful review. There are no commercial aspects to the site, I do it simply to promote interest in bridge, and do my part to help the game grow from the bottom up.

For my current readership let me introduce RABA. It is an organization that supports ACBL clubs in a 5 county area surrounding Rochester, New York. Currently there are 13 clubs that are members. Bridge is alive and well in Rochester with games available on any weekday and several evenings. While my tenure in bridge is not that long, I have played in a number of venues at all levels, and I can say that there is high quality competition in Rochester with good depth and a significant number of true experts. While some would say that I am easily entertained and would not know an expert if I saw one, it doesn't take all that much skill to know when your butt is being soundly kicked by a real master.

One thing I found unique to Rochester Bridge is that for the most part we no longer play dealt cards. RABA owns a Duplimate machine and related Dealmaster Pro software that enables the member clubs to access randomly dealt hands, all sorted into boards for their games. I do not know much about the logistics, but the software creates the hands randomly and the duplimate machine sorts the deck into 4 hands as indicated by the software. I am told that one skilled at using the system can do 24 boards in 10 minutes. So there is no shuffle and deal, you just sit down and play. As soon as the game concludes, you get a hand record equal to any I have ever seen at ACBL events. Yes, it costs money, but it the acquisition cost was funded by RABA so no individual club had to bear the capital outlay. After a short adjustment period, I think everybody enjoys the system, particularly the instant analysis provided by the hand record.

A word to everybody about how to use this site. When you click in you will see the blog with the latest post at the top. As you scroll down you can see earlier posts, but due to space limitations many of my earlier posts have been stored in the archive. You will see the archive access in the right margin of the blog page, organized by months. When you click on a month it will bring up the posts stored in that month. You can comment on any blog, and I welcome comments. I have been run over by experts, so if you have something to say, just say it. Comments go first to my Florida e-mail address where I can screen them. If the comments are of general interest and signed, I will post them unless you request that I not do so. You can also post anonymously. The comment link is at the bottom of every post. That will bring up a comment box for you to use. You can also e-mail the blog to someone else by using the envelope icon at the bottom of the blog. If you want to e-mail me, you can go to tommy@rochester.rr.com or tsolberg@tampabay.rr.com, I monitor both sites.

Under my Links, you will find one to Kitty Cooper's Bridge site. Kitty is expert at both bridge and web page design. On her site you can go to a section where she demonstrates how an expert plans and declares a hand. It is done in a format so that the reader can participate by answering questions as play proceeds. Let me know if you play the hand as well as Kitty does. Good Luck!!

Again, welcome to new readers. Thanks for coming. I have been averaging about 1 post a week, but have slowed down over the summer. I get most of my ideas at the table, so once I get back to my winter bridge schedule, I hope to have new material with increased frequency. If you have suggestions or requests, let me know.

Do You Have "Table Presence or Merely Presence at the Table?

On the completion of the auction, if an opponent asked you for a review of the auction, could you give one without hesitation or failure. If the answer is “Yes”, you are half-way toward acquiring bridge “table presence.” Well maybe 25%, because the next part (i.e. What does it all mean?) is certainly a much bigger leap. Those with table presence start the intelligence gathering process with the first action by the dealer. The process in some cases continues virtually to the end of the play. To limit the scope of the is post, I am going to focus mainly on gathering intelligence during the auction.

Let’s first define terminology: if we don’t know what table presence is, we have a slim chance of acquiring it. In a previous article I referred to the book “How the Expert’s Win at Bridge” by Bert hall and Lynn Rose-Hall. Here is what they have to say about table presence:

“People with table presence literally work out in some magical way what is going on at the table. They use inferences, deductive reasoning, and like any good poker player, they learn to read their opponents. Experts who acquire table presence concentrate on what’s going on, ask themselves the right questions, and use logic or deductive reasoning to figure out the hand and their opponents.”

The player’s that have the best table presence seem to be able to elevate the scope of their thought process, so that during the auction they appear to be thinking more about what inferences to take from the action by opponents than the problems presented by their own hand. All of us have kibitzed bridge games. Have you noticed how much easier it is to analyze the action when all you have to do is sit and watch? All of a sudden you are placing cards, values and distribution well ahead of the time that dummy is tabled. Mostly, this is because when we kibitz, we are not viewing the current deal as a problem of 13 cards, but rather 52 cards. But mystically, the ability to do this seems to disappear when we also have to manage one of the hands. This is the problem: we have to learn “to walk and chew gum at the same time.”

Albert Dormer, a noted European and British expert, in discussing table presence, said: “ We must constantly ask ourselves why the other players have done or not done what they might have done.” The reason that I included Dormer’s quotation is that it focuses not only on what other player’s have done, but more importantly on what they might have done and did not do. Every expert knows that a pass at the table gives away important information about the hand. We all process the significance of a previous pass by our partner in the auction, but the experienced player knows that often passes by opponents can be more telling than those by partner.

When I was in law school I was fortunate to enjoy the friendship of the top student in our class. Law school exams are famous for detailing intricate fact patterns, and then simply at the end asking you “discuss the legal issues.” Since I wasn’t really challenging my friend for the top spot, I simply asked him one day to tell me his secret to success with law school exams. He looked at me and said one word, “WHY?” He continued “Look at every word in the question in isolation and ask yourself why was that particular word used. His example was “Why is it a red car and not a black car?” This not only worked for me in law school exams, but I find this simple inquiry equally applicable to acquiring better table presence at bridge. The inferences that you take from asking the question “Why” are obviously important, but not half as important as the fact that you remembered to ask.

Example 1: You hold an opening hand (13 hcps). LHO deals and passes. What does that mean? He has less than 12 hpcs, he cannot preempt or make a weak 2 bid, so apparently he does not have an unbalanced hand. The remaining 27 hpcs are probably equally spread between opponents and partner. If that is the extent of your analysis that is good enough. You have limited LHO’s hand and have a start on hand distribution. Just hold onto your answer and see if it gives you guidance later in the deal.

Example 2: You are dealer, you make an opening 1 club bid. LHO passes! If he can’t muster a bid over 1 club in this day and age, you can mark him down as broke. He could not even make a lead directing overcall, so he probably does not have a decent 5 card suit. Look for partner and RHO to have the better hands. Hold onto that thought!

Example 3: Same as example 2, but LHO makes an overcall of 1 spade. At the one level he doesn’t need significant values to make this call, but mark him down for holding at least 5 spades and a suit that can take a lead by partner. Hold onto that thought!

Example 4: Your are dealer and make an opening 1 spade bid. LHO makes a 2 heart overcall. He has opening hand or compensating values, at least a 5+ card heart suit with some solid values in it, and his distribution must be 5332 or better. He has less than 17 hcps, or else he would have doubled and bid. Hold onto that thought!

Example 5: You are dealer and make an opening bid of 1 club. LHO makes a take out double. He has opening hand values and beyond that his hpcs are still unlimited. He probably has 2 or fewer clubs and relative balance in the other suits, maybe 4432. What he probably doesn’t have is a 5 card suit. Hold onto that thought!

These examples are very basic. Even a relative novice could give you the analysis given enough time. The problem is that you must think to ask the question, then make a simple analysis that you can remember, do so in the time allotted to you and finally apply the information gathered to your plan for the hand. It not easy and that is why so few people have “table presence.” On the other hand, if you do not ask the question “Why”, you are never going to make any progress.